Bhaskara-prabha

This book covers the works of Bhaskara, in particular, his monumental treatise on astronomy, the Siddhantasiroma?i, his astronomical handbook, the Kara?akutuhala, and his two mathematical treatises, the Lilavati and the Bijaga?ita, on arithmetic and algebra, respectively. It is a collection of selected papers presented at Bhaskara 900, an international conference commemorate the 900th birth anniversary of the great Indian mathematician Bhaskaracarya. Bhaskara-prabha, the radiance of Bhaskara, presents the Indian mathematical tradition and the place of Bhaskara in it. The aim of this book is to instill a sense of pride in younger generations of one of their most celebrated thinkers, by sketching some details of his mathematical achievements and capturing their imagination through his poetic flair. It is intended to raise a greater awareness among studentsand teachers of India’s rich mathematical heritage. 

Chapter 1. Ca?gadeva’s inscription of 1207.- Chapter 2. The legend of Lilavati.- Chapter 3. The poetical face of the mathematical and astronomical works of Bhaskaracarya.- Chapter 4. The lila of the Lilavati.- Chapter 5. Ga?esa Daivajña’s upapattis for some rules in the Lilavati.- Chapter 6. A study of two Malayalam commentaries on the Lilavati.- Chapter 7. Mensuration of quadrilaterals in the Lilavati.- Chapter 8. A?kapasa in the Lilavati.- Chapter 9. The Bijaga?ita of Bhaskaracarya: Some highlights.- Chapter 10. A critical study of algorithms in the Kara?i?a?vidham.- Chapter 11. Grahaga?itadhyaya of Bhaskaracarya’s Siddhantasiroma?i.- Chapter 12. Bhaskaracarya and K?ayamasa.- Chapter 13. The Vasanabha?yasof Bhaskaracarya.- Chapter 14. The production of Sines: Bhaskaracarya’s Jyotpatti.- Chapter 15. An application of the addition and subtraction formula for the Sine in Indian astronomy.- Chapter 16. Astronomical instruments in Bhaskaracarya’s Siddhantasiroma?i.- Chapter 17. Bhojaraja and Bhaskara: Precursors of Kara?akutuhala algebraic approximation formulas in the Rajam?ga?ka.- Chapter 18. Persian translations of Bhaskara’s Sanskrit texts and their impact in the following centuries.- Chapter 19. The use of Bhutasa?khyas in the Lilavati of Bhaskaracarya.- Chapter 20. Implications of Bhaskaracarya’s Lilavati to the Common Core State Standards in Mathematics.

K. RAMASUBRAMANIAN is a professor at the Cell for the Indian Science and Technology in Sanskrit, Department of Humanities and Social Sciences, Indian Institute of Technology Bombay, India. He holds a doctorate degree in Theoretical Physics, a master’s degree in Sanskrit, and a bachelor’s degree in Engineering—a weird but formidable combination of subjects to do multi-disciplinary research. He was honoured with the coveted title “Vidvat Pravara” by the Shankaracharya of Sri Sringeri Sharada Peetham, Karnataka, India, for completing a rigorous course in Advaita Vedanta (a 14-semester program), in 2003. He is one of the authors who prepared detailed explanatory notes of the celebrated works Ga?ita-yuktibha?a (rationales in mathematical astronomy), Tantrasa?graha and Kara?a-paddhati, which bring out the seminal contributions of the Kerala School of Astronomers and Mathematicians. He was conferred the prestigious award of theMaha??i Badaraya?a Vyas Samman by the then President of India, in 2008, and the R. C. Gupta Endowment Lecture Award by the National Academy of Sciences India, in 2010. He is a recipient of several other awards and coveted titles as well. From 2013, he serves as an elected council member of the International Union of History and Philosophy of Science and Technology. He is also a member of various other national and international bodies.

TAKAO HAYASHI is an emeritus professor of history of science from Doshisha University, Japan. He worked on the Bakhshali manuscript to obtain his PhD from Brown University in 1985. He focused on Indian mathematics history, and specifically the Bakhshali manuscript, the oldest surviving Indian text on mathematics. He was a fellow of the Japan Society for the Promotion of Science. He is a recipient of the Salomon Reinach Foundation Prize from French Institute (2001), Publication Prize from Mathematical Society of Japan (2005), and Kuwabara Prize fromthe History of Mathematics Society of Japan (2005). He is a member of American Mathematics Society, the Indian Society for History of Mathematics, the History of Science Society of Japan, and the Japanese Association of Indian and Buddhist Studies.

CLEMENCY MONTELLE is an associate professor at the Department of Mathematics and Statistics, University of Canterbury, New Zealand. She earned her PhD in the History of Mathematics from Brown University, in 2005. She is the joint director of History of Mathematical Sciences in India (HAMSI), a research hub devoted to the study of the astral sciences on the Indian subcontinent. Her research interest lies in the history of mathematics.